code: def main():
      """Apply Expectation Maximization on random data.
  
      Fits three randomly generated clusters into a
      Gaussian Mixture Model on Poincaré Ball.
      Then a plot function computes the probability density
      function of the GMM for visualization.
      """
      plots = expectation_maximisation_poincare_ball()
  
      plots.show()
  
file_path: geomstats/examples/plot_expectation_maximization_ball.py
imports: import os
  import matplotlib.pyplot
  import mpl_toolkits.mplot3d.art3d
  from matplotlib.patches import Circle
  import geomstats.backend
  from geomstats.geometry.poincare_ball import PoincareBall
  from geomstats.learning.expectation_maximization import GaussianMixtureModel, RiemannianEM
label_desc: Use image node_id 3 for calling a global function with example usage: main() without return types